{"paper":{"title":"The first non-zero Neumann $p-$fractional eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel M. Salort, Leandro M. Del Pezzo","submitted_at":"2014-09-02T19:45:18Z","abstract_excerpt":"In this work we study the asymptotic behavior of the first non-zero Neumann $p-$fractional eigenvalue $\\lambda_1(s,p)$ as $s\\to 1^-$ and as $p\\to\\infty.$ We show that there exists a constant $\\mathcal{K}$ such that $\\mathcal{K}(1-s)\\lambda_1(s,p)$ goes to the first non-zero Neumann eigenvalue of the $p-$Laplacian. While in the limit case $p\\to \\infty,$ we prove that $\\lambda_1(1,s)^{1/p}$ goes to an eigenvalue of the H\\\"older $\\infty-$Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0840","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}